A159798 Triangle read by rows in which row n lists n terms, starting with 1, such that the difference between successive terms is equal to n-3.

1, 1, 0, 1, 1, 1, 1, 2, 3, 4, 1, 3, 5, 7, 9, 1, 4, 7, 10, 13, 16, 1, 5, 9, 13, 17, 21, 25, 1, 6, 11, 16, 21, 26, 31, 36, 1, 7, 13, 19, 25, 31, 37, 43, 49, 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 1, 11

Offset: 1

Author

Omar E. Pol, Jul 09 2009

Keywords

• easy
• nonn
• tabl

Comments

Note that for n>1 the last term of the n-th row is the square A000290(n-2).

Row sums are n*(n^2-4*n+5)/2 = 1, 1, 3, 10, 25, 51, 91, 148, 225, ... - R. J. Mathar, Jul 17 2009, Jul 20 2009

Row sums are the positive terms of A162607. - Omar E. Pol, Jul 24 2009

Examples

			Triangle begins:
  1;
  1,  0;
  1,  1,  1;
  1,  2,  3,  4;
  1,  3,  5,  7,  9;
  1,  4,  7, 10, 13, 16;
  1,  5,  9, 13, 17, 21, 25;
  1,  6, 11, 16, 21, 26, 31, 36;
  1,  7, 13, 19, 25, 31, 37, 43, 49;
  1,  8, 15, 22, 29, 36, 43, 50, 57, 64;
  1,  9, 17, 25, 33, 41, 49, 57, 65, 73, 81;
  1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100;
		

Links

• G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

Crossrefs

Cf. A000290, A081493, A159797, A162607, A162609, A162610, A162611.

Programs

Magma

/* As triangle */ [[1 + k*(n-3): k in [0..n-1]]: n in [1..15]]; // G. C. Greubel, Apr 21 2018

Mathematica

Table[1 + k*(n-3), {n, 1, 20}, {k, 0, n-1}]// Flatten (* G. C. Greubel, Apr 21 2018 *)

PARI

for(n=1, 20, for(k=0,n-1, print1(1 + k*(n-3), ", "))) \\ G. C. Greubel, Apr 21 2018

Formula

T(n,k) = 1 + k*(n-3), 0<=kR. J. Mathar, Jul 17 2009

Extensions

More terms from R. J. Mathar, Jul 17 2009

Typo in row sums corrected by R. J. Mathar, Jul 20 2009

Edited by Omar E. Pol, Jul 24 2009